Investigating patterns in space

Space is a crowded environment where hundreds of thousands of objects travel at several kilometers per second, most of them being not controlled and subject to the effect of the drag/solar radiation pressure and Earth’s gravitational field only. On the other hand, the active objects are subject to changes in orbital elements for operational reasons, spanning from station keeping (i.e. keeping the nominal orbit/orbital slot over time) to collision avoidance maneuvers, passing through controlled re-entry.

The main source of information to keep track of the position of each object is the NORAD (North American Aerospace Defense Control) catalog, which is updated every few hours and is public, so anyone can have access to those data and eventually analyze them.

The catalog basically contains a list of TLE (Two Lines Elements), one for each of the objects being tracked by the NORAD. TLE uses a compact notation to report the satellite’s state (in form of Keplerian elements) at time of generation, and few other information useful to estimate the future position of the satellite. Since each TLE is updated over time (the update rate varies accordingly with the “importance” given to that specific object), we can keep track of all the updates. Investigating on the time evolution of each Keplerian element for any satellite of interest is useful to better understand what’s going on above us.

To carry on thus study, I downloaded the catalogs belonging to the period 1 January 2020 to 30 November 2021, with daily updates, and then I reported the coded information into Excel files for data analysis in Python. The results I’ve got are interesting indeed, showing how things happen and, sometimes, revealing very interesting patterns. Lots of things happen in space!

SSO station keeping

Sun-Synchronous Orbits (SSO) make a profitable utilization of the RAAN (right ascension of the ascending node) precession (happening due to the Earth’s oblateness) to keep aligned the orbit plane normal with the Sun vector; this has multiple advantages such as a constant illumination condition on the satellite. So, SSO orbits have to be considered as space highways, with a lot of Earth Observation satellites spending their lifetime there.

In these orbits the SMA (semimajor axis) and the inclination are strictly related?each other. For any given SMA we only have a single inclination value for defining the relevant SSO orbit.

Due to the atmospheric drag, the semimajor axis decreases over time, and this has an effect on the relative orientation of the orbital plane respect to the Sun direction. Station keeping maneuvers are needed time by time to resume the nominal SMA and restore the SSO conditions.

We here consider a couple of ESA satellites (Sentinel-1A, ID = 39634 and Sentinel-1B, ID = 41456). The Sentinel-1 mission comprises a constellation of two polar-orbiting satellites, in a sun-synchronous orbit with a 12 day repeat cycle and 175 orbits per cycle operating day and night performing C-band synthetic aperture radar imaging, enabling them to acquire imagery regardless of the weather. They both have a nominal altitude of 693 km that, being the orbit circular, corresponds to a semimajor axis of about 7071 km.

Working as a team, the two satellites are commanded to perform semimajor axis correction at the same time to keep the relative geometry. The maneuvers are executed quite often (about every 2 weeks) and have an annual repeating pattern, with a maximum SMA during summer and a minimum SMA during winter:

The slight change in SMA is due to the fact that the Earth is moving on a slightly elliptical orbit around the Sun, and this implies a slightly different precession rate to keep constant the orientation respect to the Sun.

GEO station keeping

?Satellites in geostationary orbit are subject to tangential (due to the Earth’s shape) and normal (due to the Sun and the Moon attraction) forces that gently push them away from their nominal position (often called station keeping box), operators need to perform station keeping maneuvers on regular basis.

Here I focused on Arabsat-6A (ID = 44186) for a time interval of about 6 weeks (so we can have a closer look at the data). Being the nominal satellite position at 30.5 deg East longitude, it is subject to an eastward drift, increasing the longitude over time; it is also subject to an inclination raise over time due to the third body effect.

Looking at the figure below (taken from STK), the blue arrows highlight longitude correction maneuvers (also called East-West station keeping), while the brown arrows highlight inclination correction maneuvers (also called North-South station keeping). Instead of having a specific boundary to reach before issuing the maneuvers, it’s easy to recognize weekly patterns for these corrections: this helps in managing satellites fleets from the operation standpoint (having a fixed schedule allows to plan the maneuvers in advance and organize the ground crew’s shift).

Collision Avoidance

Being space a crowded environment, collision avoidance maneuvers are becoming a sort of routine in space. Few major events (the last one being the Russian ASAT strike happened early November 2021) caused a sharp rise in the number of uncontrolled debris. While potentially any object is subject to a potential collision, I decided to analyze ISS data since more information are publicly available for it.

Normally the operators tend to perform SMA change maneuvers to avoid the collision. From my internet research, it seems that the ISS has made such avoidance measures about 30 times since 1999, including three times in 2020. In the graph below is shown the SMA value over time of the ISS, highlighting few collision avoidance maneuvers that have been made public on internet.

These maneuvers require more fuel than what is needed in nominal conditions, and more frequent refueling operations have to been performed. Also, the activity on the ISS is suspended during those alerts, often forcing astronauts to start evacuation procedures.

Controlled reentry vs decay

?All objects in LEO orbits (below 1000 km altitude) are subject to the atmospheric drag that, being a non-conservative force, reduces the altitude itself if not properly compensated. For active satellites at the end of operative life is possible to control the descent pattern in order to allow the vehicle to re-enter over a certain region (i.e. pacific ocean). An interesting use case is relevant to Starlink constellation. The constellation is currently composed by 1600 satellites, delivering fast internet connection over the word.

The figure below shows the altitude profiles of 3 different satellites launched on the same day (7th January 2020) and subject to a controlled re-entry. From the initial release orbit (about 330 km altitude) they reached the nominal altitude (about 550 km) following slightly different patterns. After being there for a while, the descent pattern started at different times, following different patterns as well. We here recognize how, during the ascent and descent phases, the satellites are taken at specific altitudes (e.g. 360 km); this is probably done to test the performances at very low altitudes (needed to reduce the latency time).

Anyway, the vast majority of the re-entry events are not controlled. A typical case is the rocket body decay. To provide an example I selected the ARIANE-42L R/B (ID = 25586), used to put in geostationary orbit PANAMSAT-6B in 1998. To accomplish such task, the launcher put the satellite in a GTO (Geosynchronous Transfer Orbit), that is highly elliptical (perigee about 300 km, apogee about 42000 km).

The picture below compares the apogee and perigee altitudes over time starting from 1st January, 2020. It shows how the perigee altitude remains constant while the apogee altitude is reduced over time due to the atmospheric drag (the effect of the drag at the perigee is to reduce the apogee altitude). The apogee took more than 20 years to drop from 36000 km to 16000 km!

Also note as the decay ratio increases in exponential manner when the apogee altitude is less than 200 km.?

The Luch

The Luch Olymp-K (ID = 40258) was launched in September 2014 with a Proton-M rocket. Differently from most of the objects in the geostationary orbit, this Russian communication satellite made a series of orbital maneuvers after it reached its destination orbital regime, varying its position relative to the Earth and causing close approaches with a multitude of communication satellites, causing concerns for espionage. The figure below shows how, from January 2020, it changed its position about 10 times:

May be this the beginning of a space war perhaps?